In this paper, the global optimization problem with an objective function that is multiextremal that satisfies the Lipschitz condition over a hypercube is considered. An algorithm that belongs to the class of information methods introduced by R.G. Strongin is proposed. The knowledge of the Lipschitz constant is not supposed. The local tuning on the behavior of the objective function and a new t...

This paper is concerned with the robust control problem of LFT (Linear Fractional Representation) uncertain systems depending on a time-varying parameter uncertainty. Our main result exploits an LMI (Linear Matrix Inequality) characterization involving scalings and Lya-punov variables subject to an additional essentially non-convex algebraic constraint. The non-convexity enters the problem in t...

Methodologyof extraction of optimal sets of logical rules using neural networks and global minimization procedures has been developed. Initial rules are extracted using density estimation neural networks with rectangular functions or multi-layered perceptron (MLP) networks trained with constrained backpropagation algorithm, transforming MLPs into simpler networks performing logical functions. A...

This thesis deals with surface extraction from noisy volumetric images, which is a common problem in medical image analysis. Due to noise, the use of a-priori information about surface topology and shape is necessary for automatic surface extraction methods. Deformable surface models can incorporate such geometric knowledge into extraction process which is restated as an energy minimization pro...

Given a finite set of m scenarios, computing a portfolio with the minimium Value-at-Risk (VaR) is computationally difficult: the portfolio VaR function is non-convex, non-smooth, and has many local minima. Instead of formulating an n-asset optimal VaR portfolio problem as minimizing a loss quantile function to determine the asset holding vector R, we consider it as a minimization problem in an ...

The phase equilibrium modeling for multi-component systems is essential in process systems engineering. In particular, phase stability analysis, Gibbs free energy minimization and estimation of parameters in thermodynamic models are challenging global optimization problems involved in phase equilibrium calculations and modeling for both reactive and non-reactive systems. To date, many significa...

The problem of minimizing a polynomial function in several variables over R n is considered and an algorithm is given. When the polynomial has a minimum the algorithm returns the global minimum and nds at least one point in every connected component of the set of minimizers. A characterization of such points is given. When the polynomial does not have a minimum the algorithm can compute its inn...

The problem of minimizing a polynomial function in several variables over Rn is considered and an algorithm is given. When the polynomial has a minimum the algorithm returns the global minimum and nds at least one point in every connected component of the set of minimizers. A characterization of such points is given. When the polynomial does not have a minimum the algorithm can compute its in m...

A numerical scheme is proposed to generate a microstructure of a martensitic material when subjected to arbitrary boundary conditions. The deformation gradient is decomposed multiplicatively into an elastic strain and a transformation strain. The elastic part ensures compatibility between the (conforming) finite elements. A global energy minimization scheme similar to Genetic Algorithms, yet su...